Following Corollary 3.3.5 and Theorem 3.11.6 in [1]}, the LCP in (REF ) has a solution from the assumption that the set \(\mathcal {V}\)  is nonempty and \(\mathbb {E}[M(\xi )]\)  is adequate or a
Z-matrix. Let \(x^*(T)\)  be a sparse solution of
the LCP in (REF ), which is defined as
\(\begin{aligned}x^*(T) \in & \quad {\rm argmin}\, \Vert x(T)\Vert _0\\& \quad {\rm s.t. } \quad \quad 0\le x(T) \perp \mathbb {E}[M(\xi )x(T)+q(\xi )] \ge 0,\end{aligned}\) 
